15 ideas
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 13342 | Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap] |
| 13251 | Each person is free to build their own logic, just by specifying a syntax [Carnap] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 3286 | An organism is conscious if and only if there is something it is like to be that organism [Nagel] |
| 3288 | Can we describe our experiences to zombies? [Nagel] |
| 4883 | Nagel's title creates an impenetrable mystery, by ignoring a bat's ways that may not be "like" anything [Dennett on Nagel] |
| 3287 | We can't be objective about experience [Nagel] |
| 4989 | Physicalism should explain how subjective experience is possible, but not 'what it is like' [Kirk,R on Nagel] |